Trinisphere's ability affects the total cost of the spell. It is applied *after* any other cost increasers or cost reducers are applied: First apply any cost increases. Next apply any cost reducers. Finally look at the amount of mana you have to pay. If it's less than three mana, you'll pay three mana.

Even with a cost reducer on the battlefield, spells can't cost less than three mana to cast.

If a spell costs at least three mana due to additional costs, such as kicker costs, that's fine.

You still need to pay any additional nonmana costs the spell has, such as sacrificing a creature or discarding cards.

Casting a creature with morph face down already costs three mana, even though the converted mana cost of the face-down spell is zero, so Trinisphere normally doesn't modify the total cost of a face-down creature spell. However, if Dream Chisel is reducing that cost while Trinisphere is on the battlefield, you'll still have to pay three mana for the spell.